More than six million Americans have now signed up for private insurance under the Affordable Care Act, according to a White House official, with just four days to go until the end of its first open enrollment period.

While traveling in Italy on Thursday, President Obama shared the news in a conference call with thousands of health-care navigators and volunteers helping enroll people on state and federal marketplaces, said the official, who asked not to be identified because the numbers had not been formally announced.

As the volume of consumers seeking health plans has surged—there were over 1.5 million visits to HealthCare.gov Wednesday and more than 430,000 calls to the marketplaces' call centers—Obama urged those on the call to work even harder to get individuals covered.

Assuming that 6-million-plus figure is official, it suggests there was a rather massive surge in sign-ups during the past few weeks. Only about 4.2 million people had signed up for coverage at the end of February, a total which didn't reach 5 million until about a week and a half ago, according to the White House.

More good news for the president and his ACA allies: The clock hasn't run out on the initial, six-month enrollment period just yet. There are still a few days left before the standard March 31 deadline, and administration officials announced earlier this week that they would extend that existing cutoff into mid-April for anyone who tried to enroll in the regular period but failed to.

Regardless, the latest total marks a significant, if somewhat symbolic, victory for the White House, which can now say that they topped the CBO's most recent projection for the number of enrollees during the law's first six months. (The original projection was in the 7 million range, but that was downgraded to 6 million after healthcare.gov's horrendous roll-out.) Still, while the total number of enrollees is serving as shorthand for the law's success, the more pressing issue may be the breakdown of how many young—presumably healthy—Americans sign up for the exchange.